Nilpotency of normal subgroups having two 𝐺-class sizes

DOI10.1090/S0002-9939-2010-10702-5zbMath1236.20036OpenAlexW2051214408MaRDI QIDQ3020350

María José Felipe, E. Alemany, Antonio Beltrán Felip

Publication date: 4 August 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10702-5

zbMATH Keywords

conjugacy classesfinite groupssolvabilitynilpotenceconjugacy class sizesnumbers of conjugates

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite nilpotent groups, (p)-groups (20D15)

Related Items (7)

Normal sections, class sizes and solvability of finite groups. ⋮ Influence of conjugacy class sizes of some elements on the structure of a finite group ⋮ Structure of normal subgroups with three \(G\)-class sizes. ⋮ Simplicity of normal subgroups and conjugacy class sizes. ⋮ Class sizes of prime-power order \(p'\)-elements and normal subgroups. ⋮ Conjugacy classes contained in normal subgroups: an overview ⋮ Normal subgroups and class sizes of elements of prime power order

Cites Work

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• On the normal subgroup with exactly two \(G\)-conjugacy class sizes.
• Theory of finite groups. An introduction
• Groups with many equal classes
• Finite Groups in Which Every Element Has Prime Power Order
• Subgroups generated by small classes in finite groups
• Prime powers as conjugacy class lengths of π-elements
• On Groups all of Whose Elements Have Prime Power Order
• On Finite Groups with Given Conjugate Types I
• Conjugacy classes in finite groups

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